Recurrent Neural Network Solver for Structural Motion Differential Equations

In the field of structural dynamic differential equations, although traditional numerical solution methods are mature, they generally have problems with high computational costs and numerous constraints. These constraints include whether the system is linear, sensitivity to time step size, limited ability to handle high-frequency responses, and limited applicability to nonlinear systems and complex dynamic environments. Therefore, this paper attempts to use a recurrent neural network (RNNs) to solve dynamic differential equations. Unlike intelligent models that require a large amount of sample data, this solver does not need samples. Instead, it constrains the loss function using the physics-informed neural network method and provides high-precision predictive solutions based on input parameters and memory parameters. The solver is applied to single-degree-of-freedom and multi-degree-of-freedom systems, including undamped and damped free vibrations as well as undamped and damped harmonic load problems. The feasibility of the model is validated based on the average relative error, with results showing that the average relative error between the model predictions and theoretical values is [Formula: see text], with a few cases reaching 1%. The relationship between network structure, learning rate, and model performance is also explored. Additionally, common activation functions perform poorly when applied to this problem, so this paper constructs a new activation function, verifying its effectiveness and efficiency through the solver and analyzing the factors influencing the model’s performance.